During the mid- and late 1930s, Mueller and her family moved often and abruptly to places such as Italy and France to evade Nazi persecution (her father was a political dissident). In 1939, at age 15, she fled Europe with her mother and sister. Her father, Fritz Neumann, had already acquired a professorship at Evansville (Ind.) College (now the University of Evansville), and the family established a residence there. It was those early experiences that inspired themes pertaining to a cultural and family history in her poems; they are often dour and explicit yet sensuously palpable.

The death of her mother in 1953 prompted Mueller to begin writing in earnest. In “When I Am Asked” she wrote,

I sat on a gray stone bench
ringed with the ingenue faces
of pink and white impatiens
and placed my grief
in the mouth of language,
the only thing that would grieve with me.

The mermaids, if that is what they are
under their full-length skirts,
sit facing each other
all down the street, more of an alley,
in front of their gray row houses.
They all look the same, like a fair-haired
order of nuns, or like prostitutes
with chaste identical faces.
How calm they are, with their vacant eyes,
their hands in laps that betray nothing.
Only one has scales on her dusky dress.

Before achieving widespread acclaim as a poet, Mueller wrote prose. Her first major publication was a book of essays printed in 1965. She also worked as a book reviewer for the Chicago Daily News before becoming a founding member of the Poetry Center of Chicago. Later Mueller frequently taught and gave lectures on creative writing at the University of Chicago, Elmhurst (Ill.) College, and Goddard College, Plainfield, Vt. Some of her other volumes of poetry include The Private Life (1976), Waving from Shore (1989), and Learning to Play by Ear (1990).

Mueller’s other literary awards include the National Book Award in 1981 for The Need to Hold Still (1980), and she was named the Illinois Poet Laureate in 1987.

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